Three Dimensional Aero-Structural Shape Optimization of Turbomachinery Blades

135 Pages·2011·12.36 MB·English

Three Dimensional Aero-Structural Shape
Optimization of Turbomachinery Blades
Vadivel Kumaran Sivashanmugam
A Thesis
in
The Department
of
Mechanical and Industrial Engineering
Presented in Partial Fulfillment of the Requirements
for the Degree of Master of Applied Science (Mechanical Engineering) at
Concordia University
Montr´eal, Qu´ebec, Canada
January 2011
(cid:13)c Vadivel Kumaran Sivashanmugam, 2011
CONCORDIA UNIVERSITY
School of Graduate Studies
This is to certify that the thesis prepared
By: Vadivel Kumaran Sivashanmugam
Entitled: Three Dimensional Aero-Structural Shape Optimization of
Turbomachinery Blades
and submitted in partial fulfilment of the requirements for the degree of
Master of Applied Science (Mechanical Engineering)
complies with the regulations of the University and meets the accepted standards
with respect to originality and quality.
Signed by the final examining committee:
Dr. Gerard J. Gouw (Chair)
Dr. Fariborz Haghighat (Ext. to Program)
Dr. Ramin Sedaghati (Examiner)
Dr. Wahid S. Ghaly (Supervisor)
Approved by
MIE Department Chair or Graduate Program Director
2011
Dean, Faculty of Engineering and Computer Science
ABSTRACT
Three Dimensional Aero-Structural Shape Optimization of Turbomachinery Blades
Vadivel Kumaran Sivashanmugam
Aero-structural optimization of gas turbine blades is a very challenging
task, given e.g. three dimensional nature of the flow, stringent performance require-
ments, structural and manufacturing considerations, etc. The current research work
addresses this challenge by development and implementation of structural shape op-
timization module and integrating it with an aerodynamic shape optimization mod-
ule to form an automated aero-structural optimization procedure. The optimizer
combines a Multi-Objective Genetic Algorithm (MOGA), with a Response Surface
Approximation (RSA) of the Artificial Neural Network (ANN) type. During the
optimization process, each objective function and constraint is approximated by an
individual ANN, which is trained and tested using an aerodynamic as well as a struc-
ture database composed of a few high fidelity flow simulations (CFD) and struc-
ture analysis (CSD) that are obtained using ANSYS Workbench 11.0. Addition
of this multiple ANN technique to the optimizer greatly improves the accuracy of
the RSA, provides control over handling different design variables and disciplines.
The described methodology is then applied to the aero-structural optimization of the
E/TU-3 turbine blade row and stage at design conditions to improve the aerodynamic
and structural performance of the turbomachinery blades by optimizing the stacking
curve. The proposed methodology proved quite successful, flexible and practical with
significant increase in stage efficiency and decrease in equivalent stress.
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ACKNOWLEDGEMENTS
I am heartily thankful to my supervisor, Dr. Wahid Ghaly, whose encour-
agement, guidance and excellent support from the initial to the final level enabled me
to develop an understanding of the subject and given me an unforgettable journey.
It is a pleasure to thank my parents who were backbone for me throughout
the life and having faith on me. They were always a great moral support in number
of ways during the hardest period of my life.
I am thankful to Ms. Leslie Hosein and Ms. Charlene Wald for their timely
administrative help, suggestion and kindness.
I offer my regards and blessings to my colleagues Raja, Mohammad Arab-
nia, Benedikt Roidl, Alfin and many others in the CFD lab who supported me in any
respect during the completion of the project.
IowemydeepestgratitudetomyfriendsinIndia,Dr. GaneshAnavardhan,
Vasanth, Sriram, Jey, Rajesh, Kamalesh, Rajini, Senthil and many other well-wishers
for their timely support, advice and having confidence on me.
Finally, I would like to thank my wife Nithya for her continued enthusiasm,
support and love. Without her support I may not followed my dream of pursuing a
career in aerospace. She is the backbone of my success.
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TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1 Introduction 1
1.1 Turbomachinery optimization . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Previous investigations . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Current work . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Numerical Implementation 12
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Numerical Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Gradient Optimization . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Non-Gradient or Direct Optimization Methods . . . . . . . . . 14
2.3 Response Surface Approximations (RSA) . . . . . . . . . . . . . . . . 20
2.3.1 Design of Experiments (DOE) . . . . . . . . . . . . . . . . . . 20
2.3.2 Artificial Neural Networks (ANN) . . . . . . . . . . . . . . . . 21
2.3.3 ANN training . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.4 ANN testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Flow Field Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5.1 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . 32
2.5.2 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Optimization Methodology 40
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
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3.2 Geometric representation . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Quadratic Rational Bezier Curve (QRBC) . . . . . . . . . . . 42
3.2.2 Design variables . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Present optimization cycle . . . . . . . . . . . . . . . . . . . . . . . . 49
4 Redesign cases 57
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 E/TU-3 Turbine Stage Redesign . . . . . . . . . . . . . . . . . . . . . 58
4.3 Geometry preparation and boundary conditions . . . . . . . . . . . . 59
4.4 Effect of design variables on turbine blade stress . . . . . . . . . . . . 60
4.5 Objectives and Constraints . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.1 Single objective structural optimization . . . . . . . . . . . . . 63
4.5.2 Multi objective aero-structural optimization . . . . . . . . . . 63
4.6 E/TU-3 turbine stage optimization . . . . . . . . . . . . . . . . . . . 65
4.6.1 Structural optimization of turbine blade with three design vari-
ables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6.2 Database enrichment and optimization . . . . . . . . . . . . . 69
4.6.3 Singlepointaero-structuralMultiobjectiveoptimizationofE/TU-
3 stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7 E/TU-3 turbine blade row optimization . . . . . . . . . . . . . . . . . 76
4.7.1 Singlepointmultiobjectiveaero-structuraloptimizationofE/TU-
3 turbine blade row . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Conclusion 110
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
vi
Bibliography 112
Appendix 119
A ANN Error Measures 120
A.1 Root mean squared Error (RMSE) . . . . . . . . . . . . . . . . . . . 120
A.2 Maximum Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.3 R squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.4 Relative Average Absolute Error (RAAE) . . . . . . . . . . . . . . . 122
A.5 Relative Maximum Absolute Error (RMAE) . . . . . . . . . . . . . . 122
A.6 Average Relative Error (ARE) . . . . . . . . . . . . . . . . . . . . . . 122
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LIST OF FIGURES
2.1 Typical flow of GA operation . . . . . . . . . . . . . . . . . . . . . . 34
2.2 A sample bio-neuron [1] . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3 A sample artificial neuron [2] . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 A sample artificial neuron [3] . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Typical training and testing trends with optimum stopping point . . 36
2.6 A typical example of over fitted and properly fitted curves [4] . . . . 37
2.7 Flow of controls: Back Propagation Neural Network . . . . . . . . . . 38
2.8 Sigmoid transfer function . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.9 Hyperbolic tangent transfer function . . . . . . . . . . . . . . . . . . 39
3.1 Aero-Structural Optimization Cycle. . . . . . . . . . . . . . . . . . . 50
3.2 Quadratic Rational Bezier Curve (QRBC) representation [5] . . . . . 51
3.3 Stacking curve parametrization using QRBC [5] . . . . . . . . . . . . 52
3.4 Aerodynamic sensitivity analysis of objective functions to design vari-
ables [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5 Structural sensitivity analysis of objective functions to design variables 54
3.6 Single ANN for all the outputs . . . . . . . . . . . . . . . . . . . . . . 55
3.7 Single ANN for each output (Concept of multiple ANNs) . . . . . . . 55
3.8 Optimization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1 Steps in getting the geometry for CFD and FEA . . . . . . . . . . . . 80
4.2 E/TU-3 Original geometry [6] . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Stress contours: E/TU-3 Original turbine blade . . . . . . . . . . . . 82
4.4 Suction side stress contours for different lean angles . . . . . . . . . . 83
4.5 Pressure side stress contours for different lean angles . . . . . . . . . 84
4.6 Suction side stress contours for different Sweep angles . . . . . . . . . 85
viii
4.7 Pressure side stress contours for different sweep angles . . . . . . . . 86
4.8 Suction side stress contours at different bowing intensity values . . . . 87
4.9 Pressure side stress contours at different bowing intensity values . . . 88
4.10 ANN training parameters and its performance variables (Errors) . . . 89
4.11 ANN training parameters and its performance variables (Updated er-
rors with 100 sample points) . . . . . . . . . . . . . . . . . . . . . . . 89
4.12 ANN training error bands (100 sample points) . . . . . . . . . . . . . 90
4.13 Genetic algorithm convergence history . . . . . . . . . . . . . . . . . 91
4.14 Suction side stress contours at different bowing intensity values . . . . 92
4.15 ANNtrainingparametersanditsperformancevariables(Errors)(updated
with 103 sample points) . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.16 ANN training error bands (103 sample points) . . . . . . . . . . . . . 93
4.17 Suction side stress contours at different bowing intensity values . . . . 94
4.18 Stacking of the optimum blade (Initial E/TU-3 shown by wire frame) 95
4.19 Original and optimized stacking line representations . . . . . . . . . . 96
4.20 Distribution of stator pressure coefficient at hub, mid-span and tip . . 97
4.21 Distribution of rotor pressure coefficient at hub, mid-span and tip . . 98
4.22 Exit flow angle comparison . . . . . . . . . . . . . . . . . . . . . . . . 99
4.23 Axial velocity comparison . . . . . . . . . . . . . . . . . . . . . . . . 99
4.24 SS flow separation and sonic surface for original & optimum stators [7] 100
4.25 Spanwise distribution of original and optimum incidence and mass flux
[7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.26 Spanwise distribution of stage loading [7] . . . . . . . . . . . . . . . . 101
4.27 Pressure side von Mises stress contour comparison . . . . . . . . . . . 102
4.28 Suction side von Mises stress contour comparison . . . . . . . . . . . 103
4.29 Hub von Mises stress contour comparison . . . . . . . . . . . . . . . . 104
4.30 Original and optimum blade shapes . . . . . . . . . . . . . . . . . . . 105
ix
4.31 Database enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.32 Comparison of stress contours on the hub surface . . . . . . . . . . . 107
4.33 Comparison of stress contours on the pressure surface . . . . . . . . . 108
4.34 Comparison of stress contours on the suction surface . . . . . . . . . 109
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